
This invention relates to a method for determining preselected performance characteristics of a tread of a tire, comprising ride comfort, noise and handling, and a tire provided with a tread having optimal characteristics with reference to said performance characteristics.
The subject of this invention is a method which allows to determine a set of performance characteristics of a tread of a tire by means of a single criterion which refers to all the performance characteristics taken into account.
An initial aspect of the invention is a method for determining preselected performance characteristics of a tread of a tire, comprising ride comfort, noise and handling, where a longitudinal direction (x), a transversal direction (y) and a vertical direction (z) are associated with said tread, where said tread has a preselected thickness and a preselected circumferential development and is made from a preselected rubber compound comprising blocks and grooves, each portion of said tread in contact with a road surface having a contact area, where said method comprises the following phases:
a) dividing said tread into a 3-D grid of full cells and empty cells of preselected dimensions (dxdydz),
b) identifying piles of said cells in said grid, each pile of cells having a base area equal to that of one cell (dxdy) and a height (h) equal to said thickness of the tread, said piles of cells being full, empty or partially fully,
c) dividing each contact area into longitudinal and transversal strips of piles of cells, with preselected dimensions in said transversal and longitudinal directions,
d) counting the number of consecutive piles of full cells delimited by two piles of cells which are either partially full or empty, one preceding, the other following said consecutive piles of full cells in each strip and
e) associating a transversal or longitudinal stiffness K with each strip of piles of cells by means of the following linear relationship:
K=m*n
where n is the number of consecutive piles of full cells and m is an angular coefficient which is determined by means of the following linear relationship:
m=mm*i+c
where mm is an angular coefficient, i is the total number of empty cells present in said two piles of cells which are either partially full or empty delimiting said consecutive piles of full cells and c is a constant, said angular coefficient mm and constant c both depending on the number n of consecutive piles of full cells,
f) assigning a preselected deformation state to each transversal and longitudinal strip of piles of cells,
g) determining at least one single force F, associated with each strip of piles of cells and acting in one of transversal (y) and longitudinal (x) directions by means of said stiffness value K and said deformation state,
h) determining at least one total force Ft associated with each contact area and acting in one of transversal (y) and longitudinal (x) said directions by summing all the single forces associated with all the transversal and longitudinal strips of piles of cells of said contact area, said total force representing at least one of said performance characteristics,
i) determining the pattern of the total forces Ft associated with all the contact areas along said circumferential development of the tread and
j) analysing said pattern of total forces Ft to evaluate whether said total forces assume values such as to optimize at least one preselected performance characteristic of said tread.
According to one embodiment:
k) in said step c), each contact area is divided into transversal strips of piles of cells with dimensions dx ly h, where dx is the length of a cell in said longitudinal direction (x), ly is the width of said strip in said transversal direction (y), measured in a preselected position in said longitudinal direction (x) and delimited by portions of the contour line of the contact area, and h is the thickness of said tread,
l) in said step e), a transversal stiffness Ky is associated with each transversal strip of piles of cells,
m) in said step g), a single transversal force Fy=Ky*y is associated with each transversal strip,
n) in said step h), a total transversal force Fyt is associated with each contact area and
o) in said step i), a pattern of the total transversal forces Fyt is obtained for the entire circumferential development of the tread and in said step j) the values assumed by said total transversal forces are evaluated to check whether they have a mean value higher than a preselected limit and a variance lower than a preselected limit to optimize said tread with reference to handling.
According to another embodiment:
p) in said step c), each contact area is divided into longitudinal strips of piles of cells with dimensions dy lx h, where dy is the width of a cell in said transversal direction (y), lx is the length of said strip in said longitudinal direction (x), measured in a preselected position in said transversal direction (y) and delimited by portions of the contour line of the contact area, and h is the thickness of said tread,
q) in said step e), a longitudinal stiffness Kx, is associated with each longitudinal strip of piles of cells and
r) in said step g), a single longitudinal force Fx=Kx*x is associated with each longitudinal strip,
s) in said step h), a total longitudinal force Fxt is associated with each contact area and
t) in said step i), a pattern of the total longitudinal forces Fxt is obtained for the entire circumferential development of the tread and in said step j) the values assumed by said total longitudinal forces are evaluated to check whether they have a mean value and variance lower than preselected limits to minimize the noise output by said tread and optimize ride comfort.
Preferably, said method also comprises the following phase:
u) associating a total transversal stiffness Kyt to each contact area by summing the transversal stiffness values Ky associated with all transversal strips in said contact area.
Advantageously, said method also comprises the following phase:
v) associating a total longitudinal stiffness Kxt to each contact area by summing the longitudinal stiffness values Kx associated with all longitudinal strips in said contact area.
Preferably, the value of said stiffness Kxt is in the range from 2300 to 2500 N/mm and the value of said stiffness Kyt is in the range from 2400 to 2600 N/mm.
In turn, the ratio of said stiffness values Kyt and Kxt is preferably as follows:
Kyt/Kxt=0.98÷1.05.
The method according to this invention has the advantage of being simple and very reliable.
A second aspect of this invention relates to a tire provided with a tread having optimal characteristics as regards preselected performance characteristics, comprising ride comfort, noise and handling, where a longitudinal direction (x), a transversal direction (y) and a vertical direction (z) are associated with said tread, where said tread has a preselected thickness and a preselected circumferential development and is made from a preselected rubber compound and comprises blocks and grooves, each portion of said tread in contact with a road surface having a contact area, where said tread is divisible into a 3-D grid of full cells and empty cells of preselected dimensions (dxdydz), where in said grid piles of said cells are identified, each pile of cells having a base area equal to that of one cell (dxdy) and height (h) equal to said thickness of the tread, said piles of cells being full, empty and partially full, where each contact area is divided into transversal and longitudinal strips of piles of cells having preselected dimensions in said transversal and longitudinal directions, where each strip of piles of cells comprises consecutive piles of full cells delimited by two piles of partially full or empty cells, one preceding and the other following said consecutive piles of full cells, where a transversal or longitudinal stiffness K is associated with each strip of piles of cells which is linearly linked to the number n of said consecutive piles of full cells by means of an angular coefficient m, said angular coefficient m being, in turn, linearly linkedxe2x80x94by means of an angular coefficient mmxe2x80x94to the total number i of empty cells in two piles of partially full or empty cells which delimit said consecutive piles of full cells, except for a constant c, said angular coefficient mm and constant c both depending on the number n of consecutive piles of full cells, where a single force F acting in one of said transversal (y) and longitudinal (x) directions is associated with each transversal and longitudinal strip of piles of cells, said force F depending on said stiffness K and a preselected state of deformation of said strip of piles of cells, where at least one total force Ft, consisting of the sum of all the single forces associated with all the transversal or longitudinal strips of piles of cells of said contact area, is associated with each contact area, said total force representing at least one of said performance characteristics, where said full and empty cells have an arrangement which is substantially uniform along the circumferential development of said tread and generates total forces associated with all the contact areas of all the portions of said tread in contact during one entire revolution, having values substantially equal and constant so to optimize at least one preselected performance characteristic of said tread.
According to an embodiment, each contact area is divisible into transversal strips of piles of cells with dimensions dx ly h, where dx is the length of a cell in said longitudinal direction (x), ly is the width of said strip in said transverse direction (y), measured in a preselected position in said longitudinal direction (x) and delimited by portions of the contour line of the contact area, and h is the thickness of said tread, a transversal stiffness Ky and a single transversal force Fy=Ky*y being associated with each transversal strip of piles of cells, a total transversal force Fyt being associated with each contact area, said total transversal force Fyt resulting from the summation of all the single forces Fy associated with all the transversal strips of said contact area, said total transversal forces Fyt having a mean value higher than a preselected limit and a variance lower than a preselected limit to optimize said tread with reference to handling.
According to another embodiment, each contact area is divisible into longitudinal strips of piles of cells with dimensions dy lx h, where dy is the width of a cell in said transversal direction (y), lx is the length of said strip in said longitudinal direction (x), measured in a preselected position in said transversal direction (y) and delimited by portions of the contour line of the contact area, and h is the thickness of said tread, a longitudinal stiffness Kx and a single longitudinal force Fx=Kx*x being associated with each longitudinal strip of piles of cells, a total longitudinal force Fxt being associated with each contact area, said total longitudinal force Fxt resulting from the summation of all the single forces Fx associated with all the longitudinal strips of said contact area, said total longitudinal forces Fxt having a mean value and a variance lower than preselected limits to minimize the noise output by said tread and optimize ride comfort.
Preferably, a total transversal stiffness value Kyt is associated with each contact area by summing the transversal stiffness values Ky associated with all transversal strips in said contact area.
Advantageously, a total longitudinal stiffness value Kxt is associated with each contact area by summing the longitudinal stiffness values Kx associated with all longitudinal strips in said contact area.
Preferably, said stiffness values Kxt and Kyt, have the aforementioned values.
In turn, the ratio between said stiffness values Kyt and Kxt has the aforementioned values.
Advantageously, said tread hasxe2x80x94for a modulus of elasticity of shear G equal to 1xe2x80x94the following stiffness values Kxt, and Kyt:
Kxt=2345 N/mm
Kyt=2412 N/mm.
In this particular case, the ratio between said stiffness values Kyt and Kxt is as follows:
xe2x80x83Kyt/Kxt=1.03.
A third aspect of this invention relates to a tire with a tread having optimal characteristics as regards preselected performance characteristics, comprising ride comfort, noise and handling, where a longitudinal direction (x), a transversal direction (y) and a vertical direction (z) are associated with said tread, where said tread has a preselected thickness and a preselected circumferential development and is made from a preselected rubber compound and comprises blocks and grooves, each portion of said tread in contact with a road surface having a contact area, where a total longitudinal stiffness value Kxt and a total transversal stiffness value Kyt are associated with each contact area, said stiffness values Kxt and Kyt having the following values:
Kxt=2300÷2500 N/mm
Kyt=2400÷2600 N/mm.
Preferably, the ratio between said stiffness values Kyt and Kxt is as follows:
Kyt/Kxt=0.98÷1.05.
Advantageously, said tread hasxe2x80x94for a modulus of elasticity of shear G equal to 1xe2x80x94the following stiffness values Kxt, and Kyt:
Kxt=2345 N/mm
Kyt=2412 N/mm.
Moreover, the ratio between said stiffness values Kyt and Kxt is as follows:
Kyt/Kxt=1.03.
A fourth aspect of this invention relates to a tire with a tread having optimal characteristics as regards preselected performance characteristics, comprising ride comfort, noise and handling, said tread having an arrangement of full cells and empty cells which is substantially uniform and equal throughout the contact areas along the circumferential development of said tread.
A fifth aspect of this invention relates to a method for determining preselected performance characteristics of a tread of a tire, comprising ride comfort, noise and handling, said method comprising the following phases:
determining, for each new tread pattern, various types of transversal and longitudinal strips of piles of cells in a contact area;
determining the angular coefficient m for each type of strip, on the basis of the number of empty cells (i) in two piles of cells which delimit it (FIG. 10);
subsequently, determining the stiffness K on the basis of the number of consecutive piles of full cells (n) in said strip (FIG. 8 or FIG. 9) and
then determining a force F associated with each strip according to the modulus of elasticity G of the type of compound used for said tread.
The method and the tire according to this invention are based on a xe2x80x9cfull and emptyxe2x80x9d evaluation criteria (full cells and empty cells) in the contact area of the tread. The contact area is divided into 3-D cells (full and empty) with dimensions dx dy dz. The cells are grouped into piles of full, empty and partially full cells with dimensions dx dy h. The piles of cells are, in turn, grouped into transversal strips (direction y) with dimensions dx ly h and longitudinal strips (direction x) with dimensions dy lx h. The corresponding transversal or longitudinal stiffness is associated with each transversal and longitudinal strip by means of the linear equations: K=m*n. The straight lines depend on the type of pile (partially full or empty) which, respectively, precedes and follows the group consecutive piles of full cells in the strip. The angular coefficients mm of these straight lines, in turn, are on a straight line which binds them to the total number i of empty cells in the two piles which delimit the groups of consecutive piles of full cells. The corresponding transversal force Fy=Ky*y or longitudinal force Fx=Kx*x is determined by applying a, for example triangular, shearing deformation state to each transversal or longitudinal strip i.e. null deformation at the start of the contact area and maximum at the end of the contact area, in the transversal or longitudinal direction. The sum of all the transversal forces andxe2x80x94respectivelyxe2x80x94of all the longitudinal forces associated with the transversal and longitudinal strips of piles of cells in the contact area respectively provides the total transversal force and the total longitudinal force corresponding to a position of the contact area. The pattern of the total transversal and longitudinal forces is then determined for all the contact areas identified in the circumferential development of the tread and the spectrum thereof is calculated to evaluate whether the values are such to optimize performance characteristics, such as comfort, noise and handling.
The ride comfort and the noise output by the treadxe2x80x94in particular the output xe2x80x9csignal volumexe2x80x9dxe2x80x94are optimized by controlling the longitudinal force.
The expression xe2x80x9csignal volumexe2x80x9d is herein used to indicate the intensity of the noise output by the tread, i.e. the absolute noise volume.
Ride comfort is optimized by minimizing the longitudinal force generated by the tread during tire rolling on any type of road surface (consequently, including irregularities of the road surface and/or isolated obstacles, i.e. manhole covers, tram tracks, etc.). In particular, the harmonic components of the longitudinal forcexe2x80x94involving frequencies between 0 and 150 Hzxe2x80x94are considered.
In turn, the noise output by the tread when rolling is minimized by means of an optimal pattern of longitudinal stiffness of the tread in its circumferential development, i.e. by means of a longitudinal force with a low mean value and limited oscillations around this value. This allows to reduce the xe2x80x9cvolumexe2x80x9d of the output noise (with equal modulus of elasticity G of the tread compound). In this case, the harmonic components of the longitudinal force involve frequencies higher than 150 Hz.
The noise output by the tire when cornering, i.e. in conditions involving leaning and vertical load transfer, is minimized taking into account the variations in length of the contact area with the vertical load. In other words, both the variations of the contact area along the circumferential development and the variations in the contact area due to rapid variations of the vertical load are taken into account.
The method according to this invention also allows to determine the slip angle (force) of the tread of a tire when cornering and the transversal stiffness of the tire. Also in this case, a brush model, known to engineers expert in the field, is used and a triangular transversal shearing (deformation is imposed) on the contact area.
Handling is optimizedxe2x80x94as concerns the contribution of the tread to the slip anglexe2x80x94by means of a high transversal stiffness of the tread involved in the contact. This is obtained by controlling the transversal stiffness Kyt of the tread.
The method according to this invention also allows to predetermine the torsional stiffness of the tread using the transversal stiffness value Ky and the longitudinal stiffness value Kx, of the strips of piles of cells. The total torque Ckt generated by a rotation imposed on the contact area is determined. The ratio between the torque and the rotation is the total torsional stiffness Ktt of the tread under contact.
A high torsional stiffness of the tread allows to additionally optimize handling. This is attained by controlling the lateral and longitudinal stiffness values and by the geometrical position of these stiffness values (i.e. of the cell of the tread to which these stiffness values refer) in the contact area.
Consequently, the type of full and empty elements allows to control the variations of longitudinal, transversal and torsional stiffness during tire rolling. These variations of stiffness influence the performance of the tire with respect to a vehicle (vibrations, handling) and the external environment (vibrations, noise).